scholarly journals Testing Hereditary Properties of Ordered Graphs and Matrices

Author(s):  
Noga Alon ◽  
Omri Ben-Eliezer ◽  
Eldar Fischer
10.37236/799 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Martin Klazar

For classes ${\cal O}$ of structures on finite linear orders (permutations, ordered graphs etc.) endowed with containment order $\preceq$ (containment of permutations, subgraph relation etc.), we investigate restrictions on the function $f(n)$ counting objects with size $n$ in a lower ideal in $({\cal O},\preceq)$. We present a framework of edge $P$-colored complete graphs $({\cal C}(P),\preceq)$ which includes many of these situations, and we prove for it two such restrictions (jumps in growth): $f(n)$ is eventually constant or $f(n)\ge n$ for all $n\ge 1$; $f(n)\le n^c$ for all $n\ge 1$ for a constant $c>0$ or $f(n)\ge F_n$ for all $n\ge 1$, $F_n$ being the Fibonacci numbers. This generalizes a fragment of a more detailed theorem of Balogh, Bollobás and Morris on hereditary properties of ordered graphs.


2006 ◽  
Vol 27 (8) ◽  
pp. 1263-1281 ◽  
Author(s):  
József Balogh ◽  
Béla Bollobás ◽  
Robert Morris

Author(s):  
József Balogh ◽  
Béla Bollobás ◽  
Robert Morris

2011 ◽  
Vol 18 (04) ◽  
pp. 611-628
Author(s):  
K. Hambrook ◽  
S. L. Wismath

A characteristic algebra for a hereditary property of identities of a fixed type τ is an algebra [Formula: see text] such that for any variety V of type τ, we have [Formula: see text] if and only if every identity satisfied by V has the property p. This is equivalent to [Formula: see text] being a generator for the variety determined by all identities of type τ which have property p. Płonka has produced minimal (smallest cardinality) characteristic algebras for a number of hereditary properties, including regularity, normality, uniformity, biregularity, right- and leftmost, outermost, and external-compatibility. In this paper, we use a construction of Płonka to study minimal characteristic algebras for the property of rectangular k-normality. In particular, we construct minimal characteristic algebras of type (2) for k-normality and rectangularity for 1 ≤ k ≤ 3.


2014 ◽  
Vol 31 (5) ◽  
pp. 1539-1554
Author(s):  
Ruijuan Li ◽  
Xinhong Zhang ◽  
Qiaoping Guo
Keyword(s):  

1994 ◽  
Vol 51 (1-2) ◽  
pp. 113-116 ◽  
Author(s):  
Jaroslav Nešetřil
Keyword(s):  

2010 ◽  
Vol 110 (16) ◽  
pp. 651-654 ◽  
Author(s):  
Ruijuan Li
Keyword(s):  

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